orthogonal expansion in hilbert space

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thandu3

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1) Find a vector in ¢^3(complex) orthogonal to (1,1,1) and (1,?,?^2) where ?=e^(2?i/3)
2) Let e_j(z)=z^j for z belongs to ¢, j belongs to z(integer).show that (e_j) that ranges from (-)infinity to (+)infinity is an orthonormal sequence in RL^2.
3) the first three legendre polynomials are P_0(x)=1, P_1(x)=x P_2(x)=(3x^2-1)/2 .show that the orthonormal vectors in L^2(-1,1) obtained by applying the Gram-Schmid process to 1,x,x^2 are scalar multiples of these.
4) Which point In the linear span of (1,?,?^2) and (1,?^2,?) where ?=e^(2?i/3), is nearest to (1,-1,1)?
These are the problems of Orthogonal expansion of Hilbert space.can anybody send me those solutions?
1) These problems are from the book “an introduction to Hilbert Find a vector in ¢^3(complex) orthogonal to (1,1,1) and (1,?,?^2) where ?=e^(2?i/3)
2) Let e_j(z)=z^j for z belongs to ¢, j belongs to z(integer).show that (e_j) that ranges from (-)infinity to (+)infinity is an orthonormal sequence in RL^2.
3) the first three legendre polynomials are P_0(x)=1, P_1(x)=x P_2(x)=(3x^2-1)/2 .show that the orthonormal vectors in L^2(-1,1) obtained by applying the Gram-Schmid process to 1,x,x^2 are scalar multiples of these.
4) Which point In the linear span of (1,?,?^2) and (1,?^2,?) where ?=e^(2?i/3), is nearest to (1,-1,1)?
These are the problems of Orthogonal expansion of Hilbert space.can anybody send me those solutions?
These problems are from the book “an introduction to Hilbert space”, young.
Problems from page 42
Problem no: 4.1,4.2,4.7,4.8 .and another additional problem 4.6
Can anyone help with these 5 prob?
 
Are you kidding? You're asking one of us to email you the solutions to 13 problems;
plus for 5 of them, we have to go out and buy a book ? :shock:
 
thandu3 said:
Can anyone help with these 5 prob? < laundry list of more than one dozen exercises snipped >
Click to expand...


Hello Thandu:

At the top of this board's index, you will find a post titled, "Read Before Posting!!".

Please, read it.

It outlines your responsibilities for seeking help at this web site.

The main points of that post are (1) we don't do your homework, and (2) you make it very difficult for people to help you when you keep your knowledge and attempts secret.

After you read your responsibilities, then please come back and show us what you've been able to accomplish so far on these exercises. It would be even better if you could also include some statements about why you're stuck.

Cheers,

~ Mark :)

 
if u are unable to do it then why u have opened such a forum? u should at least porvide some hint.if u just sujjest everyone to do this then each of the world can make such a website like yours.and answer everyone to do their work by themselves.its simply kidding.beccause i seeked for hint not for doing the whole sum.`
 
thandu3 said:
if u are unable to do it then why u have opened such a forum?
Click to expand...
I will guess from the above that you still have not read the "Read Before Posting" message. Had you done so, you would have learned that this is not a fee-based service with paid staff waiting on-hand to give guaranteed instant replies, and that, lacking any effort from the student, a reasonable person will conclude that the student needs to back up and re-study the last month or two of material. Since we cannot provide those multiplied hours of course instruction, there is little point in replying.

To get your homework done for you (which is apparently what you somehow thought this free volunteer site provided), you will need to contract with a service which offers such. Since of course these services are helping you cheat, it is not surprising that many of them are fraudulent. It is advisable that you use the credit card with the lowest limit, and check your account at least once daily.

Good luck.

Eliz.
 
thandu3 said:
1) Find a vector in ¢^3(complex) orthogonal to (1,1,1) and (1,?,?^2) where ?=e^(2?i/3)
2) Let e_j(z)=z^j for z belongs to ¢, j belongs to z(integer).show that (e_j) that ranges from (-)infinity to (+)infinity is an orthonormal sequence in RL^2.
3) the first three legendre polynomials are P_0(x)=1, P_1(x)=x P_2(x)=(3x^2-1)/2 .show that the orthonormal vectors in L^2(-1,1) obtained by applying the Gram-Schmid process to 1,x,x^2 are scalar multiples of these.
4) Which point In the linear span of (1,?,?^2) and (1,?^2,?) where ?=e^(2?i/3), is nearest to (1,-1,1)?
These are the problems of Orthogonal expansion of Hilbert space.can anybody send me those solutions?
1) These problems are from the book “an introduction to Hilbert Find a vector in ¢^3(complex) orthogonal to (1,1,1) and (1,?,?^2) where ?=e^(2?i/3)
2) Let e_j(z)=z^j for z belongs to ¢, j belongs to z(integer).show that (e_j) that ranges from (-)infinity to (+)infinity is an orthonormal sequence in RL^2.
3) the first three legendre polynomials are P_0(x)=1, P_1(x)=x P_2(x)=(3x^2-1)/2 .show that the orthonormal vectors in L^2(-1,1) obtained by applying the Gram-Schmid process to 1,x,x^2 are scalar multiples of these.
4) Which point In the linear span of (1,?,?^2) and (1,?^2,?) where ?=e^(2?i/3), is nearest to (1,-1,1)?
These are the problems of Orthogonal expansion of Hilbert space.can anybody send me those solutions?
These problems are from the book “an introduction to Hilbert space”, young.
Problems from page 42
Problem no: 4.1,4.2,4.7,4.8 .and another additional problem 4.6
Can anyone help with these 5 prob?
Click to expand...

He even gets mad and indignant.

I quoted his problem so that he cannot delete his original question - if his teacher makes an inquiry about originality of his work. It will be in cyberspace.
 
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